How do you write an equation in point-slope form for the given (–1, –3) and (4, 1)?

Jul 22, 2015

Calculate the slope of a line joining the two points, then insert this slope and one of the points into the general slope-point form to give:$\textcolor{w h i t e}{\text{XXXX}}$$y - 1 = \frac{4}{5} \left(x - 4\right)$

Explanation:

Part 1: Determine the slope
$m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{1 - \left(- 3\right)}{4 - \left(- 1\right)} = \frac{4}{5}$

Part 2: Insert this slope and point $\left(4 , 1\right)$ into the general slope-point form
general form:
$\textcolor{w h i t e}{\text{XXXX}}$$y - \hat{y} = m \left(x - \hat{x}\right)$

With the derived and given values
$\textcolor{w h i t e}{\text{XXXX}}$$y - 1 = \frac{4}{5} \left(x - 4\right)$